Our research is inspired by the recent work of [1]},
where the problem of building explainable clusterings, via standard decision trees, for both the \(k\) -means and the \(k\) -medians cost functions are studied. This paper proposes algorithms with provable approximation bounds for building explainable clusterings. In addition,
it investigates the price of explainability for
these cost functions, which is the unavoidable gap between the cost of the optimal explainable and
the optimal unconstrained
clustering. Among their results, they showed
that the price of explainability for the \(k\) -means and \(k\) -median are respectively
\(O(k^2)\)  and \(O(k)\) .
